2026 SPS P1 Q26

A school canteen sells two meal sets, Set A and Set B. The numbers of meal sets sold on Monday and Tuesday are represented by the matrix

\(Q=\begin{pmatrix}120&80\\ 150&60\end{pmatrix}\)

where the rows represent Monday and Tuesday respectively, and the columns represent Set A and Set B respectively.

Set A costs \$4.50 and Set B costs \$6.00.

1. Write down a column matrix P to represent the prices of Set A and Set B.[1]
2. Calculate QP.[1]
3. Explain what each element of the matrix QP represents.[1]
4. The canteen makes a profit of 30% of the selling price of each Set A sold and 40% of the selling price of each Set B sold.
   R is a diagonal matrix such that the elements of RP gives the profit made on each Set A and Set B meal sold.
   1. State the matrix R.[1]
   2. Find the profit made by the canteen for each of the two days, by matrix to matrix multiplication.[2]